<sigh>

The biggest game changer here will be to switch to wider higher volume tyres that are run at a pressure that corresponds to the rider's weight... running too high a pressure does little to increase your actual speed and defeats the tyres ability to absorb shocks and vibration and also effects handling.

After that check your saddle... it should also absorb shock and vibration while supporting you properly. Suspension seat posts are somewhat effective in reducing big hits (if you don't mind the pogo stick action) but can affect pedaling efficiency... it is better to learn how to ride light and let your legs and arms handle the shocks.

Bar tape and gloves can also take some of the buzz out of things.

Fact here is that the OP is riding a track bike in an urban setting and track bikes are better suited for... wait for it...the track.

A road oriented bike will have longer wheelbase and geometry that is better designed for... wait for it... the road.

If we could see the OP's bike am sure there would be more to add to this... if you are riding in an aggressive position with a deep drop from the saddle to bars you will be less able to absorb shocks as your arms will be bearing more weight and you might have numb pinkie syndrome to boot.

The stiffness of the wheels is not a factor... a properly built wheel will be stiff and have very little deflection / flex and the shock absorbing properties come from the tyre.

Better tyres with higher thread counts ride better due to them being more supple... lesser tyres have stiffer sidewalls and have a reduced ride quality in what is often a trade off for survivability.

you see me shining. mash x general electric light bulbs.

Someone educate me about this.

A sprung saddle, like a Brooks B66, would also help, especially if you ride in an upright position.